Kantor Triple Systems

Research output: ThesisDoctoral Thesis (compilation)

Abstract

The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of K-simple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. Special attention is given to all real classical cases of K-simple Kantor triple systems that can be presented in another isomorphic form, i.e. defined on tensor products of composition algebras. They are of interest in their own right and help to understand the real exceptional case. Then we consider the real exceptional K-simple Kantor triple systems. The main result of the first paper is the classification up to weak isomorphism of all real exceptional K-simple Kantor triple systems defined on tensor products of composition algebras. Also, a description of the split and the five remaining cases is given. In the second paper we develop the main result of the first paper and give a classification up to isomorphism of real simple compact Kantor triple systems defined on tensor products of composition algebras. The classification is given by presenting a unified formula for multiplication in these triples. In addition, we obtain an explicit formula for the canonical trace form for real simple compact Kantor triple systems defined on tensor products of composition algebras.

Details

Authors
  • Daniel Mondoc
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • gruppteori, fältteori, algebra, algebraic geometry, group theory, Talteori, field theory, Number Theory, Composition algebras, Jordan algebras, Kantor triple systems, Lie algebras, Jordan triple systems, algebraisk geometri
Original languageEnglish
QualificationDoctor
Awarding Institution
Award date2003 Feb 10
Publisher
  • Centre for the Mathematical sciences, Lund University
Print ISBNs91-628-5513-1
Publication statusPublished - 2002
Publication categoryResearch

Bibliographic note

Defence details Date: 2003-02-10 Time: 10:15 Place: MH:C External reviewer(s) Name: Mazorchuk, Volodymyr Title: ass. Prof Affiliation: Uppsala Univ., Uppsala, SWEDEN ---